Problem: Which of the following numbers is a factor of 168? ${4,5,9,10,11}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $168$ by each of our answer choices. $168 \div 4 = 42$ $168 \div 5 = 33\text{ R }3$ $168 \div 9 = 18\text{ R }6$ $168 \div 10 = 16\text{ R }8$ $168 \div 11 = 15\text{ R }3$ The only answer choice that divides into $168$ with no remainder is $4$ $ 42$ $4$ $168$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $168$ $168 = 2\times2\times2\times3\times7 4 = 2\times2$ Therefore the only factor of $168$ out of our choices is $4$. We can say that $168$ is divisible by $4$.